Mathematical Sciences: Artinian Rings

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This project is concerned with various aspects of artinian rings. In particular, homological properties and decompositions of modules will be examined. Under the first heading, the goals are to establish further steps towards a confirmation of the Nakayama Conjecture and the Finitistic Dimension Conjecture and a solution to the Cartan Determinant Problem. In the second category, the proposer aims at the problem of whether the rings, all of whose left modules are direct sums of finitely generated modules, are of finite representation type. The research is in the general area of ring theory. A ring is an algebraic structure having both an addition and a multiplication. These objects arise naturally and are important in many areas of mathematics and physics.